The mechanical lift uses the three point hitch arms to raise and lower the mower deck, the independent lift uses a hydraulic cylinder. Which one is better depends on you:
Benefits to mechanical:
Cheaper
Will hold the mower at the set height without a separate dial, the independent lift will leak down unless you set the mower deck height dial
Easy access lever control, the independent uses either the loader joystick or a user-mounted lever (this can be a benefit to the independent if you don't like the 3PH lever positioning).
Doesn't conflict with JD Backhoe, the independent lift must be completely removed (four bolts and a handful of hairpins)
Doesn't conflict with loader, unless you add a diverter or another valve the independent lift will steal two of your SCVs.
Benefits to independent:
Can control deck height without affecting 3PH arms, useful if you don't want to take the mower off for some jobs or if you have a 3PH mounted spreader or if you use a bagger.
It's cooler.
It's an excuse to add another set of control valves as a project.
I'm happy I got the independent lift because it forced me into a project where I learned a lot about hydraulics, but really the independent is probably a better solution for most except that it's not quite as elegant. If you intend on getting a grapple or plow you'll probably want another set of mid SCVs anyway so you can ignore the issue with the loader. The backhoe issue is probably 15 minutes of work to change to the BH, not an issue since I rarely need the hoe. Especially with Pat's EZ Hitch installed my 3PH would hit the MCS bags when mowing with the mechanical lift kit (which I used to own), now that's less of an issue. Was it worth the extra money? Probably not to most people but this is a fun hobby to me. If I farmed for a living it wouldn't be cost-justified even if you ignored the loss of value because I traded my working mechanical lift for a new independent lift.
There's lots of opinions on this, you can try searching for "independent lift" or "mech lift" and see what pops up.